I'm not sure on exact laws or workings in Canada (or the U.S., to be honest) but I'm leaning towards saying no.
The reason this is is because MOST clinics (and really, ALL clinics should) want to talk over the options with the girl, find out any health concerns that only she may know, get a urine sample to test for pregnancy (in my experience, at least, even when I wasn't sexually active they had me do a urine test before prescribing the pills), do a pelvic exam, possibly some other things. Getting hormonal birth control for the first time isn't necessarily a big deal, but just because it IS a medication that can have some nasty side effects for some people, they want to be directly dealing with the woman who will be taking the medication.
IF, however, your girlfriend already has a prescription for the birth control, and that's what you meant, then that may be a different situation and you may be able to pick it up for her. I'm not certain, though.
So, if she's never used hormonal birth control before, or even if she has but will be starting something new or restarting something, I'd recomend her being the one to handle getting it (that doesn't mean you can't drive her there or go to the clinic with her, jsut that she should be present to work out getting the medication she'll be the one taking).